Bi-Univalent Functions Associated with Class Bazilevič Functions Defined by Gregory Polynomials

In this paper, we introduce and investigate a new subclass of bi-univalent Bazilevič-type functions associated with the Gregory generating function. The proposed class is defined by means of subordination and depends on the parameters ν and α, which provides a broader framework containing several previously studied subclasses as special cases. By using the coefficient comparison method together with standard estimates for functions with positive real part, we obtain upper bounds for the initial Taylor–Maclaurin coefficients |a2| and |a3|. Furthermore, the Fekete–Szegö functional |a3−ξa22| is estimated for functions belonging to this class. Several special cases are also derived to demonstrate the connection between the present results and earlier known results related to Gregory-type bi-univalent functions.